On the Completeness and Complexity of the Lifted Dynamic Junction Tree Algorithm

TL;DR

This paper provides the first completeness and complexity analysis of the lifted dynamic junction tree algorithm (LDJT), a key exact lifted inference method for temporal probabilistic models, revealing conditions for domain liftability and efficiency gains.

Contribution

It introduces the first completeness and complexity results for LDJT, a temporal lifted inference algorithm, highlighting how temporal restrictions affect domain liftability and complexity.

Findings

LDJT's lifted width can be smaller than static treewidth in many cases.

Certain restrictions in LDJT influence domain liftability results.

The paper identifies specific cases where FO12 domain liftability must be excluded.

Abstract

For static lifted inference algorithms, completeness, i.e., domain liftability, is extensively studied. However, so far no domain liftability results for temporal lifted inference algorithms exist. In this paper, we close this gap. More precisely, we contribute the first completeness and complexity analysis for a temporal lifted algorithm, the socalled lifted dynamic junction tree algorithm (LDJT), which is the only exact lifted temporal inference algorithm out there. To handle temporal aspects efficiently, LDJT uses conditional independences to proceed in time, leading to restrictions w.r.t. elimination orders. We show that these restrictions influence the domain liftability results and show that one particular case while proceeding in time, has to be excluded from FO12 . Additionally, for the complexity of LDJT, we prove that the lifted width is in even more cases smaller than the corresponding treewidth in comparison to static inference.